Question: Simplify the following expression: $r = \dfrac{10}{3x - 8} \div \dfrac{10}{2x}$
Solution: Dividing by an expression is the same as multiplying by its inverse. $r = \dfrac{10}{3x - 8} \times \dfrac{2x}{10}$ When multiplying fractions, we multiply the numerators and the denominators. $r = \dfrac{ 10 \times 2x } { (3x - 8) \times 10}$ $r = \dfrac{20x}{30x - 80}$ Simplify: $r = \dfrac{2x}{3x - 8}$